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Scattering for the two dimensional NLS with (full) exponential nonlinearity

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The first author is supported by NSF grant DMS 1265868 and DMS-1500707
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  • We obtain global well-posedness, scattering, and global $L_t^4H_{x}^{1,4}$ spacetime bounds for energy-space solutions to the energy-subcritical nonlinear Schrödinger equation

    $iu_t+Δ u = u(e^{4π |u|^2}-1)$

    in two spatial dimensions. Our approach is perturbative; we view our problem as a perturbation of the mass-critical NLS to employ the techniques of Tao-Visan-Zhang from [25]. This permits us to combine the known spacetime estimates for mass-critical NLS proved by Dodson [12] and the work of [15] and [14] to prove corresponding spacetime estimates which imply scattering.

    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35P25.


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